Question 108155

{{{sqrt( x+6) = x+4 }}}.... both sides raise to the second power

{{{(sqrt(x+6))^2 = (x+4)^2}}}
then you will have:

{{{x+6 = x^2 + 8x + 16}}}... move all terms on one side

and you will have:

{{{x^2 + 8x + 16 - x - 6 = 0}}}

{{{x^2 + 7x + 10 = 0}}}

now you can use quadratic equation to solve the problem:

{{{x[1,2]=(-b +- sqrt (b^2 -4*a*c )) / (2*a)}}}


{{{x[1,2]=(-7 +- sqrt (7^2 -4*1*10 )) / (2*1)}}}


{{{x[1,2]=(-7 +- sqrt (49 -40 )) / 2}}}

{{{x[1,2]=(-7 +- sqrt (9 )) / 2}}}

{{{x[1,2]=(-7 +- 3) / 2}}}


{{{x[1]=(-7 + 3) / 2}}}

{{{x[1]=(-4) / 2}}}

{{{x[1]=-2}}}


{{{x[2]=(-7 - 3) / 2}}}

{{{x[2]=(-10) / 2}}}


{{{x[2]=-5}}}